Data-driven discovery is revolutionizing the modeling, prediction, and control of complex systems. This textbook brings together machine learning, engineering mathematics, and mathematical physics to integrate modeling and control of dynamical systems with modern methods in data science. It highlights many of the recent advances in scientific computing that enable data-driven methods to be applied to a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy. Aimed at advanced undergraduate and beginning graduate students in the engineering and physical sciences, the text presents a range of topics and methods from introductory to state of the art.

Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control

In this manuscript, we provide a structured and comprehensive overview of techniques to integrate machine learning with physics-based modeling. First, we provide a summary of application areas for which these approaches have been applied. Then, we describe classes of methodologies used to construct physics-guided machine learning models and hybrid physics-machine learning frameworks from a machine learning standpoint. With this foundation, we then provide a systematic organization of these existing techniques and discuss ideas for future research.

Integrating Physics-Based Modeling with Machine Learning: A Survey

Self-tuning optical systems are of growing importance in technological applications such as mode-locked fiber lasers. Such self-tuning paradigms require intelligent algorithms capable of inferring approximate models of the underlying physics and discovering appropriate control laws in order to maintain robust performance for a given objective. In this work, we demonstrate the first integration of a deep-learning (DL) architecture with model predictive control (MPC) in order to self-tune a mode-locked fiber laser. Not only can our DL-MPC algorithmic architecture approximate the unknown fiber birefringence, it also builds a dynamical model of the laser and appropriate control law for maintaining robust, high-energy pulses despite a stochastically drifting birefringence. We demonstrate the effectiveness of this method on a fiber laser that is mode-locked by nonlinear polarization rotation. The method advocated can be broadly applied to a variety of optical systems that require robust controllers.

Deep learning and model predictive control for self-tuning mode-locked lasers

Massive multiple-input–multiple-output (MIMO) communications are the focus of considerable interest in recent years. While the theoretical gains of massive MIMO have been established, implementing MIMO systems with large-scale antenna arrays in practice is challenging. Among the practical challenges associated with massive MIMO systems are increased cost, power consumption, and physical size. In this paper, we study the implementation of massive MIMO antenna arrays using dynamic metasurface antennas (DMAs), an emerging technology which inherently handles the aforementioned challenges. Specifically, DMAs realize large-scale planar antenna arrays and can adaptively incorporate signal processing methods such as compression and analog combining in the physical antenna structure, thus reducing the cost and power consumption. First, we propose a mathematical model for massive MIMO systems with DMAs and discuss their constraints compared to ideal antenna arrays. Then, we characterize the fundamental limits of uplink communications with the resulting systems and propose two algorithms for designing practical DMAs for approaching these limits. Our numerical results indicate that the proposed approaches result in practical massive MIMO systems whose performance is comparable to that achievable with ideal antenna arrays.

Dynamic Metasurface Antennas for Uplink Massive MIMO Systems

Higher order dynamic mode decomposition of noisy experimental data: The flow structure of a zero-net-mass-flux jet

Robust, continuous, and software-defined beam pattern control of holographic metamaterial antennas is necessary to realize the potential of these low-power-consumption, thin, lightweight, inexpensive antennas for consumer usage of satellite communication. We present a complete feedback control approach that enables adaptive control of the radiation pattern for the electronically scanned metamaterial antenna that is robust to measurement noise and is able to continuously optimize performance throughout changing environmental conditions and antenna characteristics. The physical size, weight, and cost advantages of the metamaterial antenna make it an attractive technology when paired with robust and adaptive on-board software strategies to optimize antenna performance and self-tune for various environmental conditions.

Extremum-seeking control of the beam pattern of a reconfigurable holographic metamaterial antenna.

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Sparse Identification of Nonlinear Dynamics (SINDy)

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Koopman operator theory: Past, present, and future

/pdf/data-driven-modeling-of-detonation-wave-interactions-in-ej169mla4w.pdf

Data-driven Modeling of Detonation Wave Interactions in Rotating Detonation Engines

A theoretical model of the mode-locking of light bullets in a planar slab waveguide array is pre- sented. The model yields three dimensional localized solutions that act as global attractors for particular parameter values. The these solutions can be con- trolled via non-uniformities in the gain applied to the array. This manipulation is robust and allows for bul- let routing as well as the production of the NAND and NOR logic gates.

/pdf/light-bullet-creation-routing-and-control-with-pl-anar-2ivrjds38u.pdf

Nathan Kutz

Papers

Extremum-seeking control of the beam pattern of a reconfigurable holographic metamaterial antenna.

Sparse Identification of Nonlinear Dynamics (SINDy)

Koopman operator theory: Past, present, and future

Data-driven Modeling of Detonation Wave Interactions in Rotating Detonation Engines

Light Bullet Creation, Routing, and Control with Pl anar Waveguide Arrays